chapter  4
32 Pages

Vascular Biomechanics

WithDhanjoo N. Ghista, Liang Zhong

CONTENTS 4.1 Scope ........................................................................................................... 114 4.2 Determination of Aortic Pressure-Time Profile along with

Aortic Stiffness and Peripheral Resistance ........................................... 114 4.2.1 Introduction ................................................................................... 114 4.2.2 Analysis of Aortic Diastolic and Systolic Pressure ................. 115 4.2.3 Diastolic Pressure Pd(t) Analysis ............................................... 117 4.2.4 Systolic Pressure Ps(t) Analysis .................................................. 118 4.2.5 Determination of P2...................................................................... 119 4.2.6 Determination of Coefficients a and b in Equation 4.7........... 119 4.2.7 Determination of the Model Parameters m and l................... 120 4.2.8 Validation of the Computed Aortic Pressure Profile ............. 122 4.2.9 Application .................................................................................... 122

4.3 Aortic Stiffness and Arterial Impedance .............................................. 124 4.3.1 Measure of Aortic Stiffness (or Arteriosclerosis)..................... 124 4.3.2 Determination of Arterial Impedance

(Another Parameter for Arteriosclerosis) from Pulse-Wave Velocity and Arterial Cross-Sectional Area ............................. 125

4.3.3 Peripheral Resistance (TPR) and Impedance (z0).................... 126 4.3.4 Implication ..................................................................................... 127

4.4 Wave Reflection (due to Step Change in Arterial Impedance)......... 129 4.5 What Happens at an Arterial Bifurcation?........................................... 130 4.6 Artery Dividing into n Branches............................................................ 133 4.7 Wave Reflection Influence on the Composite (Arterial)

Pressure Wave........................................................................................... 135 4.8 Preventing Myocardial Infarction (by Reducing the Hydraulic

Load on the LV) ........................................................................................ 140 References ........................................................................................................... 140

In this chapter, we analyze the various phenomena that occur in the cardiovascular tree [1], namely

1. how the aortic pressure waveform can be obtained from the leftventricular (LV) outflow rate into the aorta and the auscultatory diastolic and systolic blood pressures [2], as well as

2. other vascular phenomena associated with pulsatile blood flow in the arterial bed to

(a) determine the aortic constitutive property,

(b) develop the concepts of arterial impedance and peripheral resistance [3],

(c) study wave reflection,

(d) analyze what happens at arterial branching, and

(e) study how wave reflection influences the composite pressure wave and the hydraulic load on the heart [4].